This book investigates compressive sensing techniques to provide a robust and general framework
for network data analytics. The goal is to introduce a compressive sensing framework for
missing data interpolation anomaly detection data segmentation and activity recognition and
to demonstrate its benefits. Chapter 1 introduces compressive sensing including its definition
limitation and how it supports different network analysis applications. Chapter 2 demonstrates
the feasibility of compressive sensing in network analytics the authors we apply it to detect
anomalies in the customer care call dataset from a Tier 1 ISP in the United States. A
regression-based model is applied to find the relationship between calls and events. The
authors illustrate that compressive sensing is effective in identifying important factors and
can leverage the low-rank structure and temporal stability to improve the detection accuracy.
Chapter 3 discusses that there are several challenges in applying compressive sensing to
real-world data. Understanding the reasons behind the challenges is important for designing
methods and mitigating their impact. The authors analyze a wide range of real-world traces. The
analysis demonstrates that there are different factors that contribute to the violation of the
low-rank property in real data. In particular the authors find that (1) noise errors and
anomalies and (2) asynchrony in the time and frequency domains lead to network-induced
ambiguity and can easily cause low-rank matrices to become higher-ranked. To address the
problem of noise errors and anomalies in Chap. 4 the authors propose a robust compressive
sensing technique. It explicitly accounts for anomalies by decomposing real-world data
represented in matrix form into a low-rank matrix a sparse anomaly matrix an error term and a
small noise matrix. Chapter 5 addresses the problem of lack of synchronization and the authors
propose a data-driven synchronization algorithm. It can eliminate misalignment while taking
into account the heterogeneity of real-world data in both time and frequency domains. The
data-driven synchronization can be applied to any compressive sensing technique and is general
to any real-world data. The authors illustrates that the combination of the two techniques can
reduce the ranks of real-world data improve the effectiveness of compressive sensing and have
a wide range of applications. The networks are constantly generating a wealth of rich and
diverse information. This information creates exciting opportunities for network analysis and
provides insight into the complex interactions between network entities. However network
analysis often faces the problems of (1) under-constrained where there is too little data due
to feasibility and cost issues in collecting data or (2) over-constrained where there is too
much data so the analysis becomes unscalable. Compressive sensing is an effective technique to
solve both problems. It utilizes the underlying data structure for analysis. Specifically to
solve the under-constrained problem compressive sensing technologies can be applied to
reconstruct the missing elements or predict the future data. Also to solve the over-constraint
problem compressive sensing technologies can be applied to identify significant elements To
support compressive sensing in network data analysis a robust and general framework is needed
to support diverse applications. Yet this can be challenging for real-world data where noise
anomalies and lack of synchronization are common. First the number of unknowns for network
analysis can be much larger than the number of measurements. For example traffic engineering
requires knowing the complete traffic matrix between all source and destination pairs in order
to properly configure traffic and avoid congestion. However measuring the flow between all
source and destination pairs is very expensive or even i
